"Dedicado a" expresses the subject of the work; it is highly unlikely that it refers to a dedication. The sense of "dedicado" is really "devoted". In English we would just say "of". And though of course "la Inmaculada" is the Virgin, the representation of the Virgin here is that of her Immaculate Conception, and that must be specified (just as you would say the Virgin of the Rosary, or whatever), because the iconography is distinctive.



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Note added at 42 mins (2018-08-30 17:05:36 GMT)
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People do talk of works "dedicated to" a person when they mean that they depict that person, but I think this usage is inaccurate and should be avoided, because dedication in art is a different concept from subject matter.

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Note added at 1 hr (2018-08-30 17:53:09 GMT)
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It's worth remembering that although the tradition of the Immaculate Conception of the Virgin Mary goes back to medieval times, it was established as a dogma of the Catholic Church by Pius IX as late as 1854. It was also further boosted by the apparition of Lourdes in 1858, when, according to St Bernadette, the Virgin told her (in Bernadette's own Gascon dialect) "que soy era immaculada concepciou". The Immaculate Conception was therefore "in fashion" in late-nineteenth-century Catholic circles, and it's therefore quite plausible that this specific representation of the Virgin would have been chosen by a modernist artist for a Catholic chapel.